TS EAMCET · Maths · Complex Number
If \(\alpha, \beta\) are non-zero integers and \(\mathrm{z}=(\alpha+i \beta)(2+7 i)\) is a purely imaginary number, then minimum value of \(|z|^2\) is
- A \(0\)
- B \(2809\)
- C \(2808\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(2809\)
Step-by-step Solution
Detailed explanation
\(Z=(\alpha+i \beta)(2+7 i)=(2 \alpha-7 \beta)+(7 \alpha+2 \beta) i\) \(\because Z\) is purely imaginary \(\Rightarrow \operatorname{Re}(Z)=0 \Rightarrow 2 \alpha-7 \beta=0 \Rightarrow 2 \alpha=7 \beta\) also \(|Z|^2=(2 \alpha-7 \beta)^2+(7 \alpha+2 \beta)^2\)…
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